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Simplifying x2 + 3x + -2.72 = 0 Reorder the terms: -2.72 + 3x + x2 = 0 Solving -2.72 + 3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2.72' to each side of the equation. -2.72 + 3x + 2.72 + x2 = 0 + 2.72 Reorder the terms: -2.72 + 2.72 + 3x + x2 = 0 + 2.72 Combine like terms: -2.72 + 2.72 = 0.00 0.00 + 3x + x2 = 0 + 2.72 3x + x2 = 0 + 2.72 Combine like terms: 0 + 2.72 = 2.72 3x + x2 = 2.72 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 2.72 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 2.72 + 2.25 Combine like terms: 2.72 + 2.25 = 4.97 2.25 + 3x + x2 = 4.97 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 4.97 Calculate the square root of the right side: 2.229349681 Break this problem into two subproblems by setting (x + 1.5) equal to 2.229349681 and -2.229349681.Subproblem 1
x + 1.5 = 2.229349681 Simplifying x + 1.5 = 2.229349681 Reorder the terms: 1.5 + x = 2.229349681 Solving 1.5 + x = 2.229349681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 2.229349681 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.229349681 + -1.5 x = 2.229349681 + -1.5 Combine like terms: 2.229349681 + -1.5 = 0.729349681 x = 0.729349681 Simplifying x = 0.729349681Subproblem 2
x + 1.5 = -2.229349681 Simplifying x + 1.5 = -2.229349681 Reorder the terms: 1.5 + x = -2.229349681 Solving 1.5 + x = -2.229349681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -2.229349681 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.229349681 + -1.5 x = -2.229349681 + -1.5 Combine like terms: -2.229349681 + -1.5 = -3.729349681 x = -3.729349681 Simplifying x = -3.729349681Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.729349681, -3.729349681}
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